The T–>0 Metal-Insulator Transition in Rare-Earth (R = Y, Sm, Nd, Pr): Synthesis and Simulations of Bond Percolation

We report synthesis techniques and x-ray diffraction and electrical resistivity measurements on high purity bulk polycrystalline La _{1− x} R _x NiO ₃ ( R  = Y, Sm, Nd, Pr). Sol-gel pre-synthesis routes using citrate/nitrate precursors were followed by high pressure (~ 200 atm oxygen) and high temperature (800–1000°C) firings. Transport measurements suggest that the metal-insulator (M-I) transition from the metallic behavior of the nickelate with the largest rare-earth (LaNiO ₃ ) to the insulating behavior of the La _{1− x} R _x NiO ₃ alloys with smaller R ions consistently occurs in a small concentration range around x  ≈ 0.3, independent of average tolerance factor. We applied a previous model, which only assumes that all twelve bonds around each small R ion become non-conducting, to motivate large-scale bond-percolation simulations on a simple cubic lattice. We previously showed that the well-established random-occupancy result for the critical bond fraction on a simple cubic lattice, p _c ≈ 0.249, corresponds to a small R ion concentration x  ≈ 0.294. Here, we applied the Depth First Search (DFS) algorithm to numerically evaluate percolation in N x N x N lattices up to N  = 512. A notable finding is that the correlated nature of bond-breaking around small- R ions in this model results in a dramatic shift in the critical bond fraction; we find the M-I transition occurs at small- R ion concentration of x  ≈ 0.358, corresponding to a critical bond fraction for percolation of only p _c ≈ 0.171. This result quantifies how the correlation (clustering) of non-conducting bonds makes percolation appreciably easier, an intuitively appealing result.